Image watermarking based on discrete fractional fourier transforms with multiple parameters

Abstract

A watermarking algorithm based on the conventional single-parameter discrete fractional Fourier transform (DFRFT) and random phase encoding was proposed by Guo et al. in the literature. In this paper, we propose to replace the single-parameter DFRFT in that watermarking method by using other extended DFRFTs with multiple parameters, i.e., the multiple-parameter DFRFT (MPDFRFT), the random DFRFT (RDFRFT) and the reality-preserving DFRFT (Real DFRFT). Since all of the additional parameters of the employed extended DFRFTs can be used as secret keys for watermark extraction, security of the watermarking algorithm can be enhanced by our proposed methods. Besides, computation requirement can be reduced if the watermarking method employs the Real DFRFT, which is a real transform. Computer experiments are also included to show effectiveness and robustness of our proposed watermarking methods.